Nuclear Computational Science by Yousry Azmy & Enrico Sartori

Author:Yousry Azmy & Enrico Sartori
Language: eng
Format: epub
Publisher: Springer Netherlands, Dordrecht

5.3.3.2 Heat Equation Approach Based on the Finite Difference Method

It is well-known that the Doppler-broadening process is equivalent to the solution of the linear heat flow equation in a semi-infinite or infinite medium which can be described by a second-order partial differential equation of the form,

(5.56)

if the initial condition f(u, 0) is specified. It can be shown [44], via the use of Fourier transform, that the solution of Eq. 5.56 is directly identifiable with Eq. 5.34 if one sets , t = Δ m 2 and .

For reactor applications, there are two finite-difference methods in use for this purpose. One is based on the implicit finite-difference method developed by Dunford and Bramblett [45] and the other is based on the explicit finite-difference method developed by Leal and Hwang [46]. For details, the reader is referred to the respective references cited.

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